# Identifiability of Differential-Algebraic Systems

arXiv: https://arxiv.org/abs/2405.13818 · HTML: https://mlsanity.com/paper/2405.13818/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 64 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 7 of 7)

- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Data-driven Discovery of Cyber-Physical Systems](https://mlsanity.com/paper/1810.00697/) (2018)
- [On the Parameter Combinations That Matter and on Those That do Not](https://mlsanity.com/paper/2110.06717/) (2021)
- [A Bird's Eye View of Nonlinear System Identification](https://mlsanity.com/paper/1907.06803/) (2019)
- [Observers for Differential Algebraic Equation Models of Power Networks: Jointly Estimating Dynamic and Algebraic States](https://mlsanity.com/paper/2202.13254/) (2022)
- [Functional observability and subspace reconstruction in nonlinear systems](https://mlsanity.com/paper/2301.04108/) (2023)
- [Target Controllability and Target Observability of Structured Network Systems](https://mlsanity.com/paper/2309.14263/) (2023)

## Built on by (most cited first, 1 of 1)

- [SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations](https://mlsanity.com/paper/2503.05993/) (2025)

## Abstract (arXiv)

Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability. Although this problem is well studied for ordinary differential equations (ODEs), few studies have focused on the more general class of systems described by differential-algebraic equations (DAEs). Examples of DAEs include dynamical systems with algebraic equations representing conservation laws or approximating fast dynamics. This work introduces a novel identifiability test for models characterized by nonlinear DAEs. Unlike previous approaches, our test only requires prior knowledge of the system equations and does not need nonlinear transformation, index reduction, or numerical integration of the DAEs. We employed our identifiability analysis across a diverse range of DAE models, illustrating how system identifiability depends on the choices of sensors, experimental conditions, and model structures. Given the added challenges involved in identifying DAEs when compared to ODEs, we anticipate that our findings will have broad applicability and contribute significantly to the development and validation of data-driven methods for DAEs and other structure-preserving models.